BMGT 311: Chapter 10

Determining the Size of a Sample

Learning Objectives

• To understand the eight axioms underlying sample size determination with a probability sample

• To know how to compute sample size using the confidence interval approach 

• To become aware of practical considerations in sample size determination

• To be able to describe different methods used to decide sample size, including knowing whether a particular method is flawed

Key Points

• Many managers falsely believe that sample size and sample representativeness are related, but they are not.

• A sample size decision is usually a compromise between what is theoretically perfect and what is practically feasible.

• Many practitioners have a large sample bias, which is the false belief that sample size determines a sample’s representativeness.

Important Points about Sampling

• Sampling method (not sample size) is related to representativeness.

• Only a probability sample (random sample) is truly representative of a population.

• Sample size determines accuracy of findings.

• The only perfect accurate sample is a census - which is for the most part, not positive in Marketing Research

Sample Accuracy

• Sample accuracy: refers to how close a random sample’s statistic is to the true population’s value it represents

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Two Types of Error

• Non sampling error: pertains to all sources of error other than sample selection method and sample size

• Sampling error: involves sample selection and sample size

Sample Size and Accuracy

• Which is of these is more accurate?

• A large probability sample or

• A small probability sample?

• The larger a probability sample is, the more accurate it is (less sample error).

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Sample Error

• Variability refers to how similar or dissimilar responses are to a given question.

Sample Error

The Confidence Interval Method of

• Confidence interval approach: applies the concepts of accuracy, variability, and confidence interval to create a “correct” sample size

• The confidence interval approach is based upon the normal curve distribution.

• We can use the normal distribution because of the Central Limit Theorem.

Central Limit Theorem

• Since 95% of samples drawn from a population will fall within + or – 1.96 × sample error (this logic is based upon our understanding of the normal curve), we can make the following statement . . .

• If we conducted our study over and over, 1,000 times, we would expect our result to fall within a known range. Based upon this, we say that we are 95% confident that the true population value falls within this range.

Example - Page 243

Figuring out the Sample Error - Module 1 Handout

• n Values:

• n = 1,000

• n = 500

• n = 100

• n = 50

• p and q = 50

• Confidence Interval = 95% or 1.96

Figuring out the Sample Error - Module 1 Handout

• n Values:

• n = 1,000 Sample Error _____

• n = 500 Sample Error _____

• n = 100 Sample Error _____

• n = 50 Sample Error _____

• p and q = 50

• Confidence Interval = 95% or 1.96

Sample Size Formula

• Need to know

• Variability: p × q

• Acceptable margin of sample error: e

• Level of confidence: z

Standard Sample Size Formula

Example: Estimating a Sample Size

• What is the required sample size?

• Five years ago, a survey showed that 42% of consumers were aware of the company’s brand (Consumers were either “aware” or “not aware.”)

• After an intense ad campaign, management wants to conduct another survey and they want to be 95% confident that the survey estimate will be within ±5% of the true percentage of “aware” consumers in the population.

• What is n?

Example: Estimating a Sample Size

• Five years ago, a survey showed that 42% of consumers were aware of the company’s brand (Consumers were either “aware” or “not aware.”)

• After an intense ad campaign, management wants to conduct another survey and they want to be 95% confident that the survey estimate will be within ±5% of the true percentage of “aware” consumers in the population.

• Z=1.96 (95% confidence)

• p=42

• q=100-p=58

• e=5

• What is n?

Example: Estimating a Sample Size

• Five years ago, a survey showed that 42% of consumers were aware of the company’s brand (Consumers were either “aware” or “not aware.”)

• After an intense ad campaign, management wants to conduct another survey and they want to be 95% confident that the survey estimate will be within ±5% of the true percentage of “aware” consumers in the population.

• Z=1.96 (95% confidence)

• p=42

• q=100-p=58

• e=5

• What is n?

• n = 374

Chapter 10 Handout Module 2, Figure out n

First Step = Figure out z and q

Situation Confidence Level Value of z p q (100-p) Allowable Error

1 95% 1.96 65 35 3.5

2 99% 2.58 65 35 3.5

3 95% 1.96 60 40 5

4 99% 2.58 60 40 5

5 95% 1.96 50 50 4

Example 1: Page 247

Example 2: Page 247

Practical Considerations

• How to estimate variability (p times q) in the population?

• Expect the worst cast (p = 50; q = 50)

• Estimate variability

• Previous studies?

• Conduct a pilot study?

Practical Considerations

• How to determine the amount of acceptable sample error.

• Researchers should work with managers to make this decision. How much error is the manager willing to tolerate?

• See page 251 for practical example

• Researchers should work with managers to take cost into consideration in this decision.

Practical Considerations

• How to decide on the level of confidence to use.

• Researchers typically use 95% or 99%.

• Most clients would not accept a confidence interval below 95% as a representative of the overall population

Other Methods of Sample Size Determination

• Arbitrary “percentage rule of thumb”

• Conventional sample size

• Statistical analysis approach requirements

• Cost basis

Sampling from Small Populations

• With small populations, use the finite population multiplier to determine small size.

Example: Page 255

Example: Page 255

More Practice for Test Questions

• Page 258 - Question #13 - Crest Toothpaste Sample Size

• Page 247 - Sample Size Calculations Practice

• Make sure you practice and know all of the equations discussed in class

• Sample Size Margin of Error

• Sample Size Formula

• Small Population Formula